How quickly do monroe piercings close up?

My parents don't want me getting a monroe, but because they think I'll regret it or it'll be bad for when I get a job. They're thinking of letting me get it I can convince them that it'll close up if I take it out. But how long would that take? Approximetely of course. And how bad would it scar? Would it maybe just look like a birthmark or freckle?